He festooned New York City with hundreds of miles of bike lanes and dispatched chairs and picnic tables to Broadway, where cars once roamed.

But for all of Mayor Michael R. Bloomberg’s efforts to reimagine transportation in New York, critics and supporters seem to agree on the one that is most likely to define his 12 years at the city’s controls.

With the introduction of a European-style bike-share system, billed by city officials as the first new wide-scale public transportation option in more than half a century, Mr. Bloomberg’s longstanding bet on cycling has reached its climactic moment.